How does one operate these i.e. ask a specific unit to make a nuclear strike on another target?

First they have to be authorized via event.

Once nukes are authorized for a side, that side will have a specified number of nuclear strikes allowed. They can be performed by units that have equipment with nuclear strengths. The attack pop-up will have the Nuclear Attack option available for such units.

Once chemicals are authorized, all ranged equipment will be assumed to be using chemicals - making their attacks more lethal. This is especially true immediately after first authorized. The impact decays over time, though.